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Mat. Sb., 2009, Volume 200, Number 1, Pages 81–96 (Mi msb4878)  

This article is cited in 6 scientific papers (total in 6 papers)

Strong asymptotics of polynomials orthogonal with respect to a complex weight

S. P. Suetin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: For polynomials orthogonal with respect to a complex-valued weight on the closed interval $\Delta=[-1,1]$ a strong asymptotic formula in a neighbourhood of $\Delta$ is obtained. In particular, for the ‘trigonometric’ weight $\rho_0(x)=e^{ix}$, $x\in\Delta$, this formula yields a description of the asymptotic behaviour of each of the $n$ zeros of the $n$th orthogonal polynomial as $n\to\infty$. This strong asymptotic formula is deduced on the basis of Nuttall's singular integral equation.
Bibliography: 28 titles.

Keywords: Padé approximants, orthogonal polynomials, strong asymptotics.

DOI: https://doi.org/10.4213/sm4878

Full text: PDF file (627 kB)
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English version:
Sbornik: Mathematics, 2009, 200:1, 77–93

Bibliographic databases:

UDC: 517.538
MSC: Primary 42C05; Secondary 33A65, 41A21
Received: 19.03.2008

Citation: S. P. Suetin, “Strong asymptotics of polynomials orthogonal with respect to a complex weight”, Mat. Sb., 200:1 (2009), 81–96; Sb. Math., 200:1 (2009), 77–93

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. N. Tulyakov, “Difference equations having bases with powerlike growth which are perturbed by a spectral parameter”, Sb. Math., 200:5 (2009), 753–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. D. N. Tulyakov, “Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients”, Sb. Math., 201:9 (2010), 1355–1402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. M. Badkov, “Asimptoticheskie svoistva nulei ortogonalnykh trigonometricheskikh polinomov polutselykh poryadkov”, Tr. IMM UrO RAN, 19, no. 2, 2013, 54–70  mathnet  mathscinet  elib
    5. A. Deaño, “Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval”, Journal of Approximation Theory, 186 (2014), 33–63  crossref  mathscinet  zmath  isi  scopus  scopus
    6. N. R. Ikonomov, R. K. Kovacheva, S. P. Suetin, “Nuttall's integral equation and Bernshtein's asymptotic formula for a complex weight”, Izv. Math., 79:6 (2015), 1215–1234  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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